Sorry for being pedantic, but the set of rational numbers has the same cardinality (size) as the set of natural numbers, so it’s not “uncountably larger” (in fact, it’s countable). You should’ve chosen the real numbers for your example, which are uncountable.
Sorry for being pedantic, but the set of rational numbers has the same cardinality (size) as the set of natural numbers, so it’s not “uncountably larger” (in fact, it’s countable). You should’ve chosen the real numbers for your example, which are uncountable.
Sorry, that’s right, got it mixed up